Université du Maine, Le Mans

France

The objective of the filtering problem is to calculate the conditional distribution of the signal process X at a time t, given the trajectory of its noisy observation up to t. When X is a finite state Markov chain, the optimal solution is generated by an explicit nonlinear (Wonham) SDE. However no closed form expressions are known for the corresponding performance indeces - the minimal mean square error and the maximum a posteriori probability. In this talk I will discuss their precise asymptotics as the noise intensity tends to infinity.

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